Sampling Proper Colorings on Line Graphs Using $(1+o(1))Δ$ Colors
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909145704169472 |
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| author | Wang, Yulin Zhang, Chihao Zhang, Zihan |
| author_facet | Wang, Yulin Zhang, Chihao Zhang, Zihan |
| contents | We prove that the single-site Glauber dynamics for sampling proper $q$-colorings mixes in $O_Δ(n\log n)$ time on line graphs with $n$ vertices and maximum degree $Δ$ when $q>(1+o(1))Δ$. The main tool in our proof is the matrix trickle-down theorem developed by Abdolazimi, Liu and Oveis Gharan (FOCS, 2021). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_08080 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Sampling Proper Colorings on Line Graphs Using $(1+o(1))Δ$ Colors Wang, Yulin Zhang, Chihao Zhang, Zihan Data Structures and Algorithms Probability We prove that the single-site Glauber dynamics for sampling proper $q$-colorings mixes in $O_Δ(n\log n)$ time on line graphs with $n$ vertices and maximum degree $Δ$ when $q>(1+o(1))Δ$. The main tool in our proof is the matrix trickle-down theorem developed by Abdolazimi, Liu and Oveis Gharan (FOCS, 2021). |
| title | Sampling Proper Colorings on Line Graphs Using $(1+o(1))Δ$ Colors |
| topic | Data Structures and Algorithms Probability |
| url | https://arxiv.org/abs/2307.08080 |